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  • 1
    Online Resource
    Online Resource
    Cham :Springer International Publishing,
    UID:
    almahu_BV046062973
    Format: 1 Online-Ressource (viii, 112 Seiten) : , Illustrationen.
    ISBN: 978-3-030-19080-4
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-17635-8
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-17636-5
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-19137-5
    Language: English
    URL: Volltext  (URL des Erstveröffentlichers)
    URL: Volltext  (URL des Erstveröffentlichers)
    URL: Cover
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  • 2
    Online Resource
    Online Resource
    Cham :Springer International Publishing,
    UID:
    almafu_BV047690877
    Format: 1 Online-Ressource (VIII, 170 Seiten) : , Illustrationen.
    ISBN: 978-3-030-68865-3
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-68864-6
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-68866-0
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-68867-7
    Language: English
    URL: Volltext  (URL des Erstveröffentlichers)
    URL: Volltext  (URL des Erstveröffentlichers)
    URL: Volltext  (URL des Erstveröffentlichers)
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  • 3
    UID:
    almahu_BV035561530
    Format: XIII, 474 S. : , Ill., graph. Darst.
    Edition: 1. publ.
    ISBN: 978-0-521-51986-1
    Language: English
    Subjects: Mathematics
    RVK:
    RVK:
    Keywords: Partielle Differentialgleichung ; Mathematisches Modell ; MATLAB
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  • 4
    Book
    Book
    New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo :World Scientific,
    UID:
    almafu_BV045116136
    Format: xii, 447 Seiten : , Diagramme.
    ISBN: 978-981-3238-78-7
    Language: English
    Subjects: Biology , Mathematics , Medicine
    RVK:
    RVK:
    RVK:
    RVK:
    Keywords: Infektionskrankheit ; Mathematisches Modell ; Epidemiologie
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  • 5
    UID:
    almahu_BV044506432
    Format: xv, 549 Seiten : , Diagramme.
    ISBN: 978-1-119-30103-5
    Additional Edition: Erscheint auch als Online-Ausgabe, PDF ISBN 978-1-119-30105-9
    Additional Edition: Erscheint auch als Online-Ausgabe, EPUB ISBN 978-1-119-30104-2
    Language: English
    Subjects: Mathematics
    RVK:
    RVK:
    Keywords: Partielle Differentialgleichung ; Kollokationsmethode ; Spline
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  • 6
    UID:
    gbv_124528082
    Format: VIII, 587 S , graph. Darst , 26 cm
    ISBN: 0849373735
    Note: Literaturangaben
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Gewöhnliche Differentialgleichung ; Numerische Mathematik ; Algorithmus ; Partielle Differentialgleichung ; Numerische Mathematik ; Algorithmus ; Partielle Differentialgleichung ; Numerisches Verfahren ; Anfangswertproblem ; Numerische Integration
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  • 7
    UID:
    gbv_369470877
    Format: 519 S. , graph. Darst.
    ISBN: 1584884231
    Series Statement: Mathematics
    Additional Edition: Erscheint auch als Online-Ausgabe Lee, H.J. Ordinary and Partial Differential Equation Routines in C, C++, Fortran, Java, Maple, and MATLAB 2003 ISBN 9780203010518
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Differentialgleichung ; Programmierung ; Numerisches Verfahren ; Numerisches Verfahren ; Gewöhnliche Differentialgleichung ; Partielle Differentialgleichung ; Programmierung ; Lehrbuch
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  • 8
    UID:
    gbv_1014215862
    Format: 1 Online-Ressource (xii, 183-375 Seiten) , Illustrationen
    ISBN: 1681732106 , 9781681732107
    Series Statement: Synthesis lectures on mathematics and statistics #20
    Content: Partial differential equations (PDEs) are one of the most used widely forms of mathematics in science and engineering. PDEs can have partial derivatives with respect to (1) an initial value variable, typically time, and (2) boundary value variables, typically spatial variables. Therefore, two fractional PDEs can be considered, (1) fractional in time (TFPDEs), and (2) fractional in space (SFPDEs). The two volumes are directed to the development and use of SFPDEs, with the discussion divided as: Vol 1: Introduction to Algorithms and Computer Coding in R Vol 2: Applications from Classical Integer PDEs. Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann-Liouville derivative. In the second volume, the emphasis is on applications of SFPDEs developed mainly through the extension of classical integer PDEs to SFPDEs. The example applications are: Fractional diffusion equation with Dirichlet, Neumann and Robin boundary conditions Fisher-Kolmogorov SFPDE Burgers SFPDE Fokker-Planck SFPDE Burgers-Huxley SFPDE Fitzhugh-Nagumo SFPDE These SFPDEs were selected because they are integer first order in time and integer second order in space. The variation in the spatial derivative from order two (parabolic) to order one (first order hyperbolic) demonstrates the effect of the spatial fractional order [alpha] with 1 [less than or equal to] [alpha] [less than or equal to] 2. All of the example SFPDEs are one dimensional in Cartesian coordinates. Extensions to higher dimensions and other coordinate systems, in principle, follow from the examples in this second volume. The examples start with a statement of the integer PDEs that are then extended to SFPDEs. The format of each chapter is the same as in the first volume. The R routines can be downloaded and executed on a modest computer (R is readily available from the Internet)
    Content: 6. Simultaneous SFPDEs -- 6.1 Introduction -- 6.2 Simultaneous SFPDEs -- 6.2.1 Main program -- 6.2.2 ODE/MOL routine -- 6.2.3 SFPDEs output -- 6.2.4 Variation of the parameters -- 6.3 Summary and conclusions --
    Content: 7. Two sided SFPDEs -- 7.1 Introduction -- 7.2 Two-sided convective SFPDE, Caputo derivatives -- 7.2.1 Main program -- 7.2.2 ODE/MOL routine -- 7.2.3 SFPDE output -- 7.3 Two-sided convective SFPDE, Riemann-Liouville derivatives -- 7.3.1 Main program -- 7.3.2 ODE/MOL routine -- 7.3.3 SFPDE output -- 7.4 Summary and conclusions --
    Content: 8. Integer to fractional extensions -- 8.1 Introduction -- 8.2 Fractional diffusion equation -- 8.2.1 Main program, Dirchlet BCs -- 8.2.2 ODE/MOL routine -- 8.2.3 Model output -- 8.2.4 Main program, Neumann BCs -- 8.2.5 ODE/MOL routine -- 8.2.6 Model output -- 8.2.7 Main program, Robin BCs -- 8.2.8 ODE/MOL routine -- 8.2.9 Model output -- 8.3 Fractional Burgers equation -- 8.3.1 Main program, Dirchlet BCs -- 8.3.2 ODE/MOL routine -- 8.3.3 Model output -- 8.4 Fractional Fokker-Planck equation -- 8.4.1 Main program -- 8.4.2 ODE/MOL routine -- 8.4.3 Model output -- 8.5 Fractional Burgers-Huxley equation -- 8.5.1 Main program -- 8.5.2 ODE/MOL routine -- 8.5.3 Model output -- 8.6 Fractional Fitzhugh-Nagumo equation -- 8.6.1 Main program -- 8.6.2 ODE/MOL routine -- 8.6.3 Model output -- 8.7 Summary and conclusions --
    Content: Authors' biographies -- Index
    Note: Includes bibliographical references and index , Part of: Synthesis digital library of engineering and computer science
    Additional Edition: ISBN 9781681732091
    Additional Edition: Erscheint auch als Druck-Ausgabe Numerical integration of space fractional partial differental equations ; vol 2: Applications from classical integer PDEs San Rafael, California : Morgan & Claypool Publishers, 2018 ISBN 9781681732091
    Language: English
    Keywords: Electronic books
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  • 9
    Online Resource
    Online Resource
    [San Rafael, CA] : Morgan & Claypool Publishers
    UID:
    gbv_1671611063
    Format: 1 Online-Ressource (xiii, 113 Seiten) , Illustrationen
    ISBN: 9781681735702
    Series Statement: Synthesis Lectures on Biomedical Engineering #57
    Content: 1. PDE model formulation -- 1.1. PDE derivation -- 1.2. Initial conditions -- 1.3. Boundary conditions -- 1.4. Summary and conclusions
    Content: 2. Model implementation -- 2.1. Main program -- 2.2. ODE/MOL routine -- 2.3. Model output -- 2.4. Summary and conclusions
    Content: 3. Model analysis -- 3.1. Main program -- 3.2. Model output, no treatment -- 3.3. Model output, complete treatment -- 3.4. Model output, intermediate treatment -- 3.5. Total population analysis -- 3.6. Summary and conclusions
    Content: 4. Moving boundary model -- 4.1. Main program -- 4.2. Model output -- 4.3. Summary and conclusions
    Content: A. Functions dss004, dss044 -- A.1. Function dss004 -- A.2. Function dss044.
    Content: This book has a two-fold purpose: (1) An introduction to the computer-based modeling of influenza, a continuing major worldwide communicable disease. (2) The use of (1) as an illustration of a methodology for the computer-based modeling of communicable diseases. For the purposes of (1) and (2), a basic influenza model is formulated as a system of partial differential equations (PDEs) that define the spatiotemporal evolution of four populations: susceptibles, untreated and treated infecteds, and recovereds. The requirements of a well-posed PDE model are considered, including the initial and boundary conditions. The terms of the PDEs are explained. The computer implementation of the model is illustrated with a detailed line-by-line explanation of a system of routines in R (a quality, open-source scientific computing system that is readily available from the Internet). The R routines demonstrate the straightforward numerical solution of a system of nonlinear PDEs by the method of lines (MOL), an established general algorithm for PDEs. The presentation of the PDE modeling methodology is introductory with a minumum of formal mathematics (no theorems and proofs), and with emphasis on example applications. The intent of the book is to assist in the initial understanding and use of PDE mathematical modeling of communicable diseases, and the explanation and interpretation of the computed model solutions, as illustrated with the influenza model
    Note: Includes bibliographical references and index
    Additional Edition: ISBN 9781681735719
    Language: English
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  • 10
    UID:
    b3kat_BV046881134
    Format: vii, 181 Seiten , Diagramme
    ISBN: 9780367224837
    Content: Mathematical models stated as systems of partial differential equations (PDEs) are broadly used in biology, chemistry, physics and medicine (physiology). These models describe the spatial and temporial variations of the problem system dependent variables, such as temperature, chemical and biochemical concentrations and cell densities, as a function of space and time (spatiotemporal distributions).For a complete PDE model, initial conditions (ICs) specifying how the problem system starts and boundary conditions (BCs) specifying how the system is defined at its spatial boundaries, must also be included for a well-posed PDE model. In this book, PDE models are considered for which the physical boundaries move with time. For example, as a tumor grows, its boundary moves outward. In atherosclerosis, the plaque formation on the arterial wall moves inward, thereby restricting blood flow with serious consequences such as stroke and myocardial infarction (heart attack).These two examples are considered as applications of the reported moving boundary PDE (MBPDE) numerical method (algorithm). The method is programmed in a set of documented routines coded in R, a quality, open-source scientific programming system. The routines are provided as a download so that the reader/analyst/researcher can use MFPDE models without having to first study numerical methods and computer programming.
    Note: 1. PDE Model Formulation. 2. PDE Model Implementation. 3. PDE Model Output. 4. Tumor growth. 5. Plaque Formation in Atherosclerosis. Appendix A1. Test of Spline Regridding. Appendix A2. Test of Moving Boundary Algorithm Spline Formulation. Appendix A3. Test of Moving Boundary Algorithm Finite Difference Formulation.
    Additional Edition: Erscheint auch als Online-Ausgabe ISBN 978-0-42927-512-8
    Language: English
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